AP® Physics 1 & 2

Gravitational Force for Enlarging Spheres

APPH12-4B9JTF

Two identical spheres are touching. Both spheres are enlarged simultaneously, while their densities remain constant. The initial gravitational force between them is ${F}_{0}$and their initial radii are ${r}_{0}$.

Which relationship, as a function of $r$, represents the magnitude of the gravitational force as the radius of the spheres is increased?